Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 27 May 2017, 04:23

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Math problem involving powers and smallest possible value

Author Message
Intern
Joined: 24 Sep 2009
Posts: 3
Followers: 0

Kudos [?]: 1 [1] , given: 0

Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 10:53
1
KUDOS
00:00

Difficulty:

(N/A)

Question Stats:

100% (02:50) correct 0% (00:00) wrong based on 5 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, what is the smallest possible positive value of n?

a. 25
b. 27
c. 45
d. 75
e. 125

thanks!!!
VP
Joined: 05 Mar 2008
Posts: 1469
Followers: 11

Kudos [?]: 277 [1] , given: 31

Re: Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 11:11
1
KUDOS
I'm getting D: 75

If both 5^2 and 3^3 are factors of n * 2^5 * 6^2 * 7^3, what is the smallest possible positive value of n?

Therefore, (n)(2^5)(3^2*2^2)(7^3)

We need two 5's and 3 3's total
There are already 2 3's so we still need two 5's and one more 3 (5*5*3) = 75
Manager
Joined: 11 Sep 2009
Posts: 129
Followers: 6

Kudos [?]: 362 [1] , given: 6

Re: Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 11:11
1
KUDOS

This is a question relating to prime factorability (is that a word?).

Basically, for any number, X, to be a factor of another number, Y, the prime factors of X must be present in the prime factors of Y. For example, if you reduce the number 50 = (5^2)*(2^1), it is a factor of any number which has these prime factors when reduced.

So, for 5^2 and 3^3 to be factors of this number, the number, when reduced to prime factors, must contain 5^2 and 3^3.

$$n*2^5*6^2*7^3$$

$$= n*2^5*(3^2*2^2)*7^3$$

$$= n*2^7*3^2*7^3$$

As seen by the above equation, we need at least one more factor of 3, as well as two more factors of 5. As a result:

n = 5^2 * 3
= 75
Intern
Joined: 24 Sep 2009
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 11:14
yeah, the answer is 75, but I'm not sure how you worked that out...
VP
Joined: 05 Mar 2008
Posts: 1469
Followers: 11

Kudos [?]: 277 [1] , given: 31

Re: Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 11:22
1
KUDOS
Think of it this way:

You have the equation 10x. What is the smallest number x can be for the equation to be a multiple of 3 (for 3 to be a factor of the equation)?

5*2*x. So for the equation to be divisible by 3 there must be a 3 in the equation. Therefore x = 3

5*2*3 is divisible by 3

Now you have the equation 15x and want to know what is the smallest number x for it to be divisible by 3^2 (or 9)
15x = 5*3*x

There is already one three in the equation. You will need at least one more 3 to factor out the 9. The smallest value of x is 3 for the number to be divisible by 9

Therefore
5*3*3 = 45

Prime factorization

Last edited by lagomez on 24 Sep 2009, 11:23, edited 1 time in total.
Intern
Joined: 24 Sep 2009
Posts: 3
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Math problem involving powers and smallest possible value [#permalink]

### Show Tags

24 Sep 2009, 11:22
sorry, I got the explanation, I didn't see all the responses! thanks
Re: Math problem involving powers and smallest possible value   [#permalink] 24 Sep 2009, 11:22
Display posts from previous: Sort by